Log-concavity and the maximum entropy property of the Poisson distribution

Abstract

We prove that the Poisson distribution maximises entropy in the class of ultra-log-concave distributions, extending a result of Harremoës. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is a concave function along this semigroup.

16 pages: revised version, accepted by Stochastic Processes and their Applications

References in corpus (2)

• Log-concavity and LC-positivity
• Preservation of log-concavity on summation

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